Error Functions

Contents

Error Functions#

The error function is a special function related to the normal distribution.

erf(x)#

Error function.

Parameters:

x (Real) – The value to take the error function of.

Definition:

\(\mathrm{erf}(x) = \dfrac{2}{\sqrt{\pi}} \displaystyle\int_0^x e^{-t^2} \, dt\)

Domain:

\((-\infty, \infty)\)

Range:

\((-1, 1)\)

Returns:

The value of \(\mathrm{erf}(x)\).

Return type:

Real

erfc(x)#

Complementary error function.

Parameters:

x (Real) – The value to take the complementary error function of.

Definition:

\(\mathrm{erfc}(x) = 1 - \mathrm{erf}(x)\)

Domain:

\((-\infty, \infty)\)

Range:

\((0, 2)\)

Returns:

The value of \(\mathrm{erfc}(x)\).

Return type:

Real